{"id":"https://openalex.org/W2004399813","doi":"https://doi.org/10.1002/1521-3870(200010)46:4<543::aid-malq543>3.0.co;2-e","title":"Graph Coloring and Reverse Mathematics","display_name":"Graph Coloring and Reverse Mathematics","publication_year":2000,"publication_date":"2000-10-01","ids":{"openalex":"https://openalex.org/W2004399813","doi":"https://doi.org/10.1002/1521-3870(200010)46:4<543::aid-malq543>3.0.co;2-e","mag":"2004399813"},"language":"en","primary_location":{"id":"doi:10.1002/1521-3870(200010)46:4<543::aid-malq543>3.0.co;2-e","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1521-3870(200010)46:4<543::aid-malq543>3.0.co;2-e","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"MLQ","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091663311","display_name":"James H. Schmerl","orcid":"https://orcid.org/0000-0003-0545-8339"},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James H. Schmerl","raw_affiliation_strings":["Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009, U. S. A","Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009, U. S. A","institution_ids":["https://openalex.org/I140172145"]},{"raw_affiliation_string":"Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009, U.S.A","institution_ids":["https://openalex.org/I140172145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091663311"],"corresponding_institution_ids":["https://openalex.org/I140172145"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.13478196,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"46","issue":"4","first_page":"543","last_page":"548"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9523000121116638,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9523000121116638,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9430000185966492,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8683743476867676},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5658189058303833},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.5657770037651062},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5584598779678345},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4730079472064972},{"id":"https://openalex.org/keywords/list-coloring","display_name":"List coloring","score":0.4315776526927948},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2318035066127777},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.20737570524215698}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8683743476867676},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5658189058303833},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.5657770037651062},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5584598779678345},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4730079472064972},{"id":"https://openalex.org/C199594403","wikidata":"https://www.wikidata.org/wiki/Q1130404","display_name":"List coloring","level":5,"score":0.4315776526927948},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2318035066127777},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.20737570524215698}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/1521-3870(200010)46:4<543::aid-malq543>3.0.co;2-e","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1521-3870(200010)46:4<543::aid-malq543>3.0.co;2-e","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"MLQ","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4297911588","https://openalex.org/W2212115383","https://openalex.org/W2546620014","https://openalex.org/W4291316360","https://openalex.org/W2380525562","https://openalex.org/W2793500002","https://openalex.org/W2585997002","https://openalex.org/W4380300356","https://openalex.org/W3169197204","https://openalex.org/W4311345810"],"abstract_inverted_index":{"Improving":[0],"a":[1],"theorem":[2],"of":[3],"Gasarch":[4],"and":[5],"Hirst,":[6],"we":[7],"prove":[8],"that":[9],"if":[10],"2":[11],"\u2264":[12,14],"k":[13],"m":[15],"<":[16],"\u03c9,":[17],"then":[18],"the":[19],"following":[20],"is":[21,31],"equivalent":[22],"to":[23],"WKL0":[24],"over":[25],"RCA0":[26],"Every":[27],"locally":[28],"k-colorable":[29],"graph":[30],"m-colorable.":[32]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-07T14:30:12.667765","created_date":"2025-10-10T00:00:00"}